Research On Extend Finite Element Method And Its Application In Simulation Of Fracture Propagation Of Rock Mass

Faults,joints and fractures are widely distributed in rock masses.These discontinuities of existence and development have great effect on the whole strength,deformation and stability of rock masse.So studying the evolvement of initiation,propagation and coalescence from some primary flaws are of great significance in theory and practice for estimating the safety and reliability of rock mass engineering.The extended finite element method(XFEM)is an effective method for discontinuous problems.Since the unique advantage of XFEM for fracture analysis,it has been employed to simulate the hydraulic fracture and crack propagation of rock mass.Supporting by the National Natural Science Foundation of China “the interactions among slopes,dams and reservoirs,the mechanisms of slope stability evolution” and National Basic Research Program of China “study of deformation-failure process of rock slope under rainfall condition and prediction model”,the basic theory of XFEM and its application in simulating crack propagation are studied deeply.The numerical model of solving the frictional contact problem and hydraulic fracture propagation are developed by XFEM.The calculation model is applied in practical engineering to investigate the mechanism of failure evolution process of mass rock.The main jobs of this paper are as follows:(1)The effect of coefficient of friction between the crack surfaces on crack tip stress field is considered and the fracture angle of compression-shear mixed-mode crack is deduced according to the maximum circumferential stress criterion.According to the failure characteristics of the crack tip of rocks forced in two directions,the compression-shear fracture criterion of rock considering frictional effect for closed crack propagation are obtained by use of maximum circumferential stress criterion and modified Griffith strength theory.(2)The extended finite element method(XFEM)is a numerical method for modeling discontinuities within a classical finite element framework.Based on the algorithm of XFEM,the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor(SIF)are discussed,and the proper parameters to calculate the SIF are given.The results from the case analysis demonstrate that the crack path is the most sensitive to the crack growth increment size,and the crack path is not mesh-sensitive.A reanalysis method for the XFEM has been introduced.The example presented shows that there is a significantly reduced computational cost for each iteration of crack growth achieved by using the reanalysis method and the reanalysis approach has increasing benefits as the mesh density increases or the value of crack growth increments size decreases.(3)A nonlinear complementary model for frictional elastic contact problems with the XFEM is presented.The conditions that describe frictional contact are formulated as a system of non-smooth equations based on variational inequality theory,and the non-smooth damped newton method is given based on the definitions of generalized derivative to directly solve the system of equations without any extra parameters and iteration.Finally,numerical examples are presented to demonstrate the correctness and effectiveness of this method.The results indicate that the method has high computational accuracy and fast convergence,and can simulate the adhesion and slide of a contact interface.(4)The extended finite element method is presented for hydro-mechanical modeling of impermeable discontinuities in rock.The governing equation of XFEM for hydraulic fracture modeling is derived by the virtual work principle of the fracture problem considering the water pressure on crack surface.Then the implement method of XFEM for hydraulic fracture modeling is deduced.The coupling relationship between water pressure gradient on crack surface and fracture opening width is obtained by semi-analytical and semi-numerical method.This method simplifies coupling analysis iteration and improves computational precision.Finally,the efficiency of the proposed method for modeling hydraulic fracture problems is verified by two examples and the advantages of the XFEM for hydraulic fracturing analysis are displayed.(5)The extended finite element method is used to solve some geotechnical problems,such as deformation and failure of jointed rock slopes,modeling fracture propagation of gravity dam foundation and hydraulic fracturing of hydraulic tunnels.The crack propagation in the rock can be modeled by XFEM with minimal remeshing after crack propagation and the trajectory of crack propagation can be explicitly described by XFEM.The proposed method is applied to simulate the fracture process of rock mass under the action of water pressure and it can reflect the interaction between fissure water and cracking in rock.Considering the contact model in XFEM,the vector sum analysis method has been introduced in XFEM and this method is applied in the stability analysis for the jointed rock slope.It is shown that the calculating process of the safety factor is simple and avoids iterations.